<!-- XHTML 1.0 Strict -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<meta name="author" content="Rachid Touzani" />
<meta name="keywords" content=" css, dropdowns, dropdown menu, drop-down, menu, navigation, nav, horizontal, vertical left-to-right, vertical right-to-left, horizontal linear, horizontal upwards, cross browser, internet explorer, ie, firefox, safari, opera, browser, lwis" />
<meta name="description" content="Clean, standards-friendly, modular framework for dropdown menus" />
<link href="../css/dropdown.vertical.css" media="screen" rel="stylesheet" type="text/css" />
<link href="../css/default.ultimate.css" media="screen" rel="stylesheet" type="text/css" />
<head>
<!-- Title -->
<title>OFELI - Documentation</title>
<!-- Stylesheet -->
<link rel="stylesheet" type="text/css" href="../doxygen.css" />
<link rel="stylesheet" type="text/css" href="../tabs.css" />
</head>
<body>
<p align="center">
  <img src="../im/ofeli.gif" alt="OFELI's Logo" width="300" height="90">
</p>
<p align="center"><font color="#203F5B" size="4" face="verdana,Helvetica">
<b>An Object Oriented Finite Element Library</b></font></p>
<!-- Complete Page-->
<div id="main">
<div id="mainmenu">
 <div class="text">
<!-- Menu -->
 <div class="tabs">
  <ul class="tablist">
   <li><a href="../index.html"><span>Home</span></a>
    <li><a href="../overview.html"><span>Overview</span></a>
    <li><a href="../extlib.html"><span>External Libraries</span></a>
    <li><a href="../citing.html"><span>Citing OFELI</span></a>
    <li><a href="../fformats.html"><span>File Formats</span></a>
    <li><a href="../demos.html"><span>Demo Codes</span></a>
  </ul>
 </div>
<!-- Generated by Doxygen 1.8.11 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
  <div id="navrow1" class="tabs">
    <ul class="tablist">
      <li><a href="index.html"><span>Main&#160;Page</span></a></li>
      <li><a href="modules.html"><span>Modules</span></a></li>
      <li><a href="namespaces.html"><span>Namespaces</span></a></li>
      <li class="current"><a href="annotated.html"><span>Classes</span></a></li>
      <li>
        <div id="MSearchBox" class="MSearchBoxInactive">
        <span class="left">
          <img id="MSearchSelect" src="search/mag_sel.png"
               onmouseover="return searchBox.OnSearchSelectShow()"
               onmouseout="return searchBox.OnSearchSelectHide()"
               alt=""/>
          <input type="text" id="MSearchField" value="Search" accesskey="S"
               onfocus="searchBox.OnSearchFieldFocus(true)" 
               onblur="searchBox.OnSearchFieldFocus(false)" 
               onkeyup="searchBox.OnSearchFieldChange(event)"/>
          </span><span class="right">
            <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
          </span>
        </div>
      </li>
    </ul>
  </div>
  <div id="navrow2" class="tabs2">
    <ul class="tablist">
      <li><a href="annotated.html"><span>Class&#160;List</span></a></li>
      <li><a href="classes.html"><span>Class&#160;Index</span></a></li>
      <li><a href="hierarchy.html"><span>Class&#160;Hierarchy</span></a></li>
      <li><a href="functions.html"><span>Class&#160;Members</span></a></li>
    </ul>
  </div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
$(document).ready(function(){initNavTree('classOFELI_1_1Line3.html','');});
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="summary">
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="classOFELI_1_1Line3-members.html">List of all members</a>  </div>
  <div class="headertitle">
<div class="title">Line3 Class Reference<div class="ingroups"><a class="el" href="group__OFELI.html">OFELI</a><a class="el" href="group__OFELI.html">OFELI</a> &raquo;  &#124; <a class="el" href="group__Shape.html">Shape Function</a></div></div>  </div>
</div><!--header-->
<div class="contents">

<p>To describe a 3-Node quadratic planar line finite element.  
 <a href="classOFELI_1_1Line3.html#details">More...</a></p>
<div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Line3:</div>
<div id="dynsection-0-summary" class="dynsummary" style="display:block;">
</div>
<div id="dynsection-0-content" class="dyncontent" style="display:none;">
 <div class="center">
  <img src="classOFELI_1_1Line3.png" usemap="#Line3_map" alt=""/>
  <map id="Line3_map" name="Line3_map">
<area href="classOFELI_1_1FEShape.html" title="Parent class from which inherit all finite element shape classes. " alt="FEShape" shape="rect" coords="0,0,64,24"/>
</map>
 </div></div>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a99475466e181befa6c9945ad6f7b69c3"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a99475466e181befa6c9945ad6f7b69c3"></a>
&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Line3.html#a99475466e181befa6c9945ad6f7b69c3">Line3</a> ()</td></tr>
<tr class="memdesc:a99475466e181befa6c9945ad6f7b69c3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor. <br /></td></tr>
<tr class="separator:a99475466e181befa6c9945ad6f7b69c3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa0e7b53b4e54bc1a6f300551cb2e43b1"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aa0e7b53b4e54bc1a6f300551cb2e43b1"></a>
&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Line3.html#aa0e7b53b4e54bc1a6f300551cb2e43b1">Line3</a> (const <a class="el" href="classOFELI_1_1Element.html">Element</a> *el)</td></tr>
<tr class="memdesc:aa0e7b53b4e54bc1a6f300551cb2e43b1"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor for an element. <br /></td></tr>
<tr class="separator:aa0e7b53b4e54bc1a6f300551cb2e43b1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a55bcc26c9827bb23af6c4a32d49541ce"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a55bcc26c9827bb23af6c4a32d49541ce"></a>
&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Line3.html#a55bcc26c9827bb23af6c4a32d49541ce">Line3</a> (const <a class="el" href="classOFELI_1_1Side.html">Side</a> *sd)</td></tr>
<tr class="memdesc:a55bcc26c9827bb23af6c4a32d49541ce"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor for a side. <br /></td></tr>
<tr class="separator:a55bcc26c9827bb23af6c4a32d49541ce"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8368f9346c9049f10c95da3388a0196d"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a8368f9346c9049f10c95da3388a0196d"></a>
&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Line3.html#a8368f9346c9049f10c95da3388a0196d">~Line3</a> ()</td></tr>
<tr class="memdesc:a8368f9346c9049f10c95da3388a0196d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Destructor. <br /></td></tr>
<tr class="separator:a8368f9346c9049f10c95da3388a0196d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a19b4776d30b04b5fa427b8e8ce732122"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a19b4776d30b04b5fa427b8e8ce732122"></a>
void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Line3.html#a19b4776d30b04b5fa427b8e8ce732122">setLocal</a> (<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> s)</td></tr>
<tr class="memdesc:a19b4776d30b04b5fa427b8e8ce732122"><td class="mdescLeft">&#160;</td><td class="mdescRight">Initialize local point coordinates in element. <br /></td></tr>
<tr class="separator:a19b4776d30b04b5fa427b8e8ce732122"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4bca61134358cac278c05031b7afb0b9"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classOFELI_1_1LocalVect.html">LocalVect</a>&lt; <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;, 3 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Line3.html#a4bca61134358cac278c05031b7afb0b9">DSh</a> () const </td></tr>
<tr class="memdesc:a4bca61134358cac278c05031b7afb0b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return partial derivatives of shape functions of element nodes.  <a href="#a4bca61134358cac278c05031b7afb0b9">More...</a><br /></td></tr>
<tr class="separator:a4bca61134358cac278c05031b7afb0b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad5af4f17aea53c0ab1e8ce2494f23234"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ad5af4f17aea53c0ab1e8ce2494f23234"></a>
<a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Line3.html#ad5af4f17aea53c0ab1e8ce2494f23234">getLocalPoint</a> () const </td></tr>
<tr class="memdesc:ad5af4f17aea53c0ab1e8ce2494f23234"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return actual coordinates of localized point. <br /></td></tr>
<tr class="separator:ad5af4f17aea53c0ab1e8ce2494f23234"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abf13023b750b4a215814cfb805b145da"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="abf13023b750b4a215814cfb805b145da"></a>
<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#abf13023b750b4a215814cfb805b145da">Sh</a> (size_t i) const </td></tr>
<tr class="memdesc:abf13023b750b4a215814cfb805b145da"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return shape function of node <code>i</code> at given point. <br /></td></tr>
<tr class="separator:abf13023b750b4a215814cfb805b145da"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4fc79aaeb587148410021052f410d4dc"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#a4fc79aaeb587148410021052f410d4dc">Sh</a> (size_t i, <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; s) const </td></tr>
<tr class="memdesc:a4fc79aaeb587148410021052f410d4dc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate shape function of node <code>i</code> at a given point <code>s</code>.  <a href="#a4fc79aaeb587148410021052f410d4dc">More...</a><br /></td></tr>
<tr class="separator:a4fc79aaeb587148410021052f410d4dc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0f35cc59cf2218efd06b13c2487f31cc"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#a0f35cc59cf2218efd06b13c2487f31cc">getDet</a> () const </td></tr>
<tr class="memdesc:a0f35cc59cf2218efd06b13c2487f31cc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return determinant of jacobian.  <a href="#a0f35cc59cf2218efd06b13c2487f31cc">More...</a><br /></td></tr>
<tr class="separator:a0f35cc59cf2218efd06b13c2487f31cc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a802168de29d5e265ee01a57fd98793e8"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a802168de29d5e265ee01a57fd98793e8"></a>
<a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#a802168de29d5e265ee01a57fd98793e8">getCenter</a> () const </td></tr>
<tr class="memdesc:a802168de29d5e265ee01a57fd98793e8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return coordinates of center of element. <br /></td></tr>
<tr class="separator:a802168de29d5e265ee01a57fd98793e8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a565411b0254679f383549c1a09bf2352"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#a565411b0254679f383549c1a09bf2352">getLocalPoint</a> (const <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &amp;s) const </td></tr>
<tr class="memdesc:a565411b0254679f383549c1a09bf2352"><td class="mdescLeft">&#160;</td><td class="mdescRight">Localize a point in the element.  <a href="#a565411b0254679f383549c1a09bf2352">More...</a><br /></td></tr>
<tr class="separator:a565411b0254679f383549c1a09bf2352"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>To describe a 3-Node quadratic planar line finite element. </p>
<p>Defines geometric quantities associated to 3-node quadratic element <code>P<sub>2</sub></code> in the space. The reference element is the segment <code>[-1,1]</code>. The user must take care to the fact that determinant of jacobian and other quantities depend on the point in the reference element where they are calculated. For this, before any utilization of shape functions or jacobian, function <b><a class="el" href="classOFELI_1_1Line3.html#a19b4776d30b04b5fa427b8e8ce732122" title="Initialize local point coordinates in element. ">setLocal()</a></b> must be invoked.<br />
<a class="el" href="classOFELI_1_1Element.html" title="To store and treat finite element geometric information. ">Element</a> nodes are ordered as the following: the left one, the central one and the right one.</p>
<dl class="section author"><dt>Author</dt><dd>Rachid Touzani </dd></dl>
<dl class="section copyright"><dt>Copyright</dt><dd>GNU Lesser Public License </dd></dl>
</div><h2 class="groupheader">Member Function Documentation</h2>
<a class="anchor" id="a4bca61134358cac278c05031b7afb0b9"></a>
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="classOFELI_1_1LocalVect.html">LocalVect</a>&lt;<a class="el" href="structOFELI_1_1Point.html">Point</a>&lt;<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&gt;,3&gt; DSh </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
        </tr>
      </table>
</div><div class="memdoc">

<p>Return partial derivatives of shape functions of element nodes. </p>
<dl class="section return"><dt>Returns</dt><dd><a class="el" href="classOFELI_1_1LocalVect.html" title="Handles small size vectors like element vectors. ">LocalVect</a> instance of partial derivatives of shape functions <em>e.g.</em> <code>dsh(i)</code>.x, <code>dsh(i)</code>.y, are partial derivatives of the <em>i</em>-th shape function. </dd></dl>
<dl class="section note"><dt>Note</dt><dd>The local point at which the derivatives are computed must be chosen before by using the member function setLocal </dd></dl>

</div>
</div>
<a class="anchor" id="a4fc79aaeb587148410021052f410d4dc"></a>
<div class="memitem">
<div class="memproto">
<table class="mlabels">
  <tr>
  <td class="mlabels-left">
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> Sh </td>
          <td>(</td>
          <td class="paramtype">size_t&#160;</td>
          <td class="paramname"><em>i</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td>
          <td class="paramname"><em>s</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td> const</td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inherited</span></span>  </td>
  </tr>
</table>
</div><div class="memdoc">

<p>Calculate shape function of node <code>i</code> at a given point <code>s</code>. </p>
<dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramdir">[in]</td><td class="paramname">i</td><td>Local node label </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">s</td><td><a class="el" href="structOFELI_1_1Point.html" title="Defines a point with arbitrary type coordinates. ">Point</a> in the reference triangle where the shape function is evaluated </td></tr>
  </table>
  </dd>
</dl>

</div>
</div>
<a class="anchor" id="a0f35cc59cf2218efd06b13c2487f31cc"></a>
<div class="memitem">
<div class="memproto">
<table class="mlabels">
  <tr>
  <td class="mlabels-left">
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> getDet </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inherited</span></span>  </td>
  </tr>
</table>
</div><div class="memdoc">

<p>Return determinant of jacobian. </p>
<p>If the transformation (Reference element -&gt; Actual element) is not affine, member function <b>setLocal()</b> must have been called before in order to calcuate relevant quantities. </p>

</div>
</div>
<a class="anchor" id="a565411b0254679f383549c1a09bf2352"></a>
<div class="memitem">
<div class="memproto">
<table class="mlabels">
  <tr>
  <td class="mlabels-left">
      <table class="memname">
        <tr>
          <td class="memname"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt;<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&gt; getLocalPoint </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &amp;&#160;</td>
          <td class="paramname"><em>s</em></td><td>)</td>
          <td> const</td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inherited</span></span>  </td>
  </tr>
</table>
</div><div class="memdoc">

<p>Localize a point in the element. </p>
<p>Return actual coordinates where <code>s</code> are coordinates in the reference element. </p>

</div>
</div>
</div><!-- contents -->
</div><!-- doc-content -->

</div> <!-- class text -->
</div> <!-- main menu -->
<!-- Google Search -->
<br><br>
<center>
  <div id="cse" style="width: 80%;">Loading</div>
  <script src="http://www.google.com/jsapi" type="text/javascript"></script>
  <script type="text/javascript"> 
     google.load('search', '1', {language : 'en', style : google.loader.themes.SHINY});
     google.setOnLoadCallback(function() {
        var customSearchOptions = {};  var customSearchControl = new google.search.CustomSearchControl(
        '012396140824982761142:-qrywxcfi_o', customSearchOptions);
        customSearchControl.setResultSetSize(google.search.Search.FILTERED_CSE_RESULTSET);
        customSearchControl.draw('cse');
     }, true);
   </script>
   <style type="text/css">
     .gsc-control-cse {
     font-family: Verdana, sans-serif;
     border-color: #DAE0E5;
     background-color: #DAE0E5;
   }
   .gsc-control-cse .gsc-table-result { font-family: Verdana, sans-serif; }
   input.gsc-input { border-color: #B6BEC5; }
   input.gsc-search-button {
     border-color: #B6BEC5;
     background-color: #D0D1D4;
   }
   .gsc-tabHeader.gsc-tabhInactive {
     border-color: #999999;
     background-color: #EEEEEE;
   }
   .gsc-tabHeader.gsc-tabhActive {
     border-color: #999999;
     background-color: #999999;
   }
   .gsc-tabsArea { border-color: #999999; }
   .gsc-webResult.gsc-result,
   .gsc-results .gsc-imageResult {
     border-color: #FFFFFF;
     background-color: #FFFFFF;
   }
   .gsc-webResult.gsc-result:hover,
   .gsc-imageResult:hover {
     border-color: #D2D6DC;
     background-color: #EDEDED;
   }
   .gsc-webResult.gsc-result.gsc-promotion:hover {
     border-color: #D2D6DC;
     background-color: #EDEDED;
   }
   .gs-webResult.gs-result a.gs-title:link,
   .gs-webResult.gs-result a.gs-title:link b,
   .gs-imageResult a.gs-title:link,
   .gs-imageResult a.gs-title:link b { color: #0568CD; }
   .gs-webResult.gs-result a.gs-title:visited,
   .gs-webResult.gs-result a.gs-title:visited b,
   .gs-imageResult a.gs-title:visited,
   .gs-imageResult a.gs-title:visited b { color: #0568CD; }
   .gs-webResult.gs-result a.gs-title:hover,
   .gs-webResult.gs-result a.gs-title:hover b,
   .gs-imageResult a.gs-title:hover,
   .gs-imageResult a.gs-title:hover b { color: #0568CD; }
   .gs-webResult.gs-result a.gs-title:active,
   .gs-webResult.gs-result a.gs-title:active b,
   .gs-imageResult a.gs-title:active,
   .gs-imageResult a.gs-title:active b { color: #0568CD; }
   .gsc-cursor-page { color: #0568CD; }
   a.gsc-trailing-more-results:link { color: #0568CD; }
   .gs-webResult .gs-snippet,
   .gs-imageResult .gs-snippet,
   .gs-fileFormatType { color: #5F6A73; }
   .gs-webResult div.gs-visibleUrl,
   .gs-imageResult div.gs-visibleUrl { color: #5F6A73; }
   .gs-webResult div.gs-visibleUrl-short { color: #5F6A73; }
   .gs-webResult div.gs-visibleUrl-short { display: none; }
   .gs-webResult div.gs-visibleUrl-long { display: block; }
   .gs-promotion div.gs-visibleUrl-short { display: none; }
   .gs-promotion div.gs-visibleUrl-long { display: block; }
   .gsc-cursor-box { border-color: #FFFFFF; }
   .gsc-results .gsc-cursor-box .gsc-cursor-page {
      border-color: #999999;
      background-color: #FFFFFF;
      color: #0568CD;
   }
   .gsc-results .gsc-cursor-box .gsc-cursor-current-page {
      border-color: #999999;
      background-color: #999999;
      color: #0568CD;
   }
   .gsc-webResult.gsc-result.gsc-promotion {
      border-color: #D2D6DC;
      background-color: #D0D1D4;
   }
   .gsc-completion-title { color: #0568CD; }
   .gsc-completion-snippet { color: #5F6A73; }
   .gs-promotion a.gs-title:link,
   .gs-promotion a.gs-title:link *,
   .gs-promotion .gs-snippet a:link { color: #0066CC; }
   .gs-promotion a.gs-title:visited,
   .gs-promotion a.gs-title:visited *,
   .gs-promotion .gs-snippet a:visited { color: #0066CC; }
   .gs-promotion a.gs-title:hover,
   .gs-promotion a.gs-title:hover *,
   .gs-promotion .gs-snippet a:hover { color: #0066CC; }
   .gs-promotion a.gs-title:active,
   .gs-promotion a.gs-title:active *,
   .gs-promotion .gs-snippet a:active { color: #0066CC; }
   .gs-promotion .gs-snippet,
   .gs-promotion .gs-title .gs-promotion-title-right,
   .gs-promotion .gs-title .gs-promotion-title-right *  { color: #333333; }
   .gs-promotion .gs-visibleUrl,
   .gs-promotion .gs-visibleUrl-short { color: #5F6A73; }
   </style>
</center>
<!-- End of Google Search Box -->
<br><br><br></p>
<div id="foot_bar">
  Copyright &copy; 1998-2019 Rachid Touzani&nbsp;
</div>
</div> <!-- main -->
</body>
</HTML>
